Weak symmetry in naturally reductive homogeneous nilmanifolds

DOI10.1216/rmjm/1181069901zbMath1055.22005OpenAlexW2050894349MaRDI QIDQ1880978

Jorge Lauret

Publication date: 27 September 2004

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069901

zbMATH Keywords

Riemannian metricnilmanifoldnaturally reductiveweakly symmetriccommutative space

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25) (L^1)-algebras on groups, semigroups, etc. (43A20)

Cites Work

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• Weakly symmetric groups of Heisenberg type
• Isometry groups on homogeneous nilmanifolds
• Weakly symmetric spaces and spherical varieties
• Modified \(H\)-type groups and symmetric-like Riemannian spaces
• Homogeneous nilmanifolds attached to representations of compact Lie groups
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• The orbit method and Gelfand pairs, associated with nilpotent Lie groups
• Naturally Reductive Homogeneous Riemannian Manifolds
• On Gelfand Pairs Associated with Solvable Lie Groups
• Commutative Spaces Which are Not Weakly Symmetric
• Gelfand pairs attached to representations of compact Lie groups